Beyond the 'superior tone' that the intuitionist might adopt (borrowing a Kantian term used to describe Jacobian realism, which posits that we have an intuition of the thing in itself), this doctrine can rely on a compelling argument, initially formulated in moral intuitionism:
1/ A moral statement cannot be derived solely from non-moral statements.
2/ Therefore, for a moral statement to be derived from other assertions, those assertions must include moral statements.
3/ Consequently, for a moral belief to be inferentially justified, its justification must involve other moral beliefs.
4/ However, to avoid infinite regression or circular reasoning, the process of inferential justification must reach an endpoint.
5/ Therefore, some moral beliefs must be self-evident. ¹

This reasoning can be applied to the axiological domain as follows:
1/ A value judgement can only be justified based on another value judgement (or axiological belief).
2/ However, to avoid infinite regression or circular reasoning, the process of inferential justification must reach an endpoint.
3/ Therefore, some axiological beliefs must be self-evident.

This explains why axiological intuitionism is an appealing doctrine. Firstly, intuitionism eliminates the problem entirely, freeing the human mind from a burden it had felt unable to bear. Secondly, it grants everyone the remarkable ability to discern what is valuable and what is not—a power as extraordinary as the ability to predict tomorrow’s weather.
It should be noted that I use 'axiological intuitionism' in a broad sense, encompassing not only doctrines that posit the existence of an intuition within us that immediately grasps values, but also value theories that rely on the obvious—that is, on value judgements recognised as self-evident. This broad definition leads me to classify as 'intuitionists' thinkers who may not have explicitly identified themselves as such.

It now seems fitting to ask the intuitionist what their intuition reveals about the value of things: namely, what holds value and what constitutes the universal hierarchy.

1. Dictionnaire d'éthique et de philosophie morale, article « Moral realism »